Unit 11: Introduction to Sequences and Series
In this final unit, we will introduce the basics of defining, notating, and evaluating sequences and series. You will explore arithmetic sequences, geometric sequences, and series, and you will learn to distinguish between them.
Completing this unit should take you approximately 2 hours.
Upon successful completion of this unit, you will be able to:
- write the terms of a sequence given a formula;
- write the formula for a sequence given the first few terms or a recursive relationship; and
- apply the formulas for arithmetic and geometric series.
11.1: Sequences and Their Notations
If you plan to learn calculus, this introduction to sequences and series will be very helpful. The first topic you will explore is how to write the terms of a sequence given a formula.
In this section, you will learn what a recursive formula is and apply it to find the terms of a recursively defined sequence.
11.2: Arithmetic Sequences
We will explore two kinds of sequneces in this unit. The first is the arithmetic sequence. In this section, you will learn the characteristics of arithmetic sequences and use a formula to find the terms.
Now, we will learn how to find the terms of an arithmetic sequence given a recursive formula.
11.3: Geometric Sequences
We continue with geometric sequences. Now, we'll cover the characteristics and terms of a geometric sequence.
Finally, we will find the terms of a geometric sequence given a recursive formula.
11.4: Geometric Series
At the last stop on our journey, we will learn the basic properties of an arithmetic series. We will also learn how to use standard notations to express series.
Finally, we will use formulas to find the terms of a geometric series.